Get a different anchor, try maybe a hollow wall anchor with the expansion wings. I would try metal.

Did you happen to hit a stud? That may be why the anchor didn't go in and just shredded the drywall.

If so, you can just use a regular screw for an extremely solid anchor into the stud.

When I get home from work I'll see if the hole is in the stud. The problem is that the position of the hole is exactly where I would need to place the anchor for the bookshelf. I've researched online about filling in drywall holes. I'm going to guess that I'm going to have to use an anchor that is long enough to penetrate through the spackle and into the material behind it.

This is where I'm stuck - If I didn't hit a stud, could I proceed like users Nidnay and Millworkman are suggesting, and use a metallic anchor with wings? Or, if I DID hit a stud like greg_2015, can I just fill in the hole and then use a long screw to penetrate the spackle and anchor it into the remaining material behind it? I'm just worried that the wall structure has been compromised too much and will result in the screw pulling out from the wall and creating a dangerous situation.

Sorry everyone, I know this sounds convoluted! Thanks for the help so far!

You can just spackle it and retry. I'd suggest drilling a hole in the spackle after it sets so that it's more neat and tidy and less likely to chip off again when you insert the screw or toggle bolt.

If it's a stud, then you need to know if it's a wooden or metal stud so that you can use the right type of screw. With a stud, the support is the stud itself and not the drywall/patch, so a spackled fix isn't a big deal.

If it isn't a stud, then using the toggle bolts shown above will spread the support out over a wider area on the back of the drywall, so a spackled fix isn't a big deal (as long as the metal wings go beyond the fix, which I assume it would).

Note that there are all different types of toggle bolts. The one shown above is probably one of the more simple ones and is probably fine for this job since there isn't that much weight on your shelves (all of the weight is on the legs. The wall attachments are just keeping it from falling over).

There's a brand called 'snap toggle' that is pretty easy to use (not that any of them are hard) but are a little more expensive. I think they're pretty heavy duty too, if that would set your mind at ease. Do a search on Youtube to see how they're used, if you have any doubts.

I guess it's also possible that you hit something else in your wall. HVAC ducts or water pipes or something else. If that's the case, then you're out of luck with this project. You'll have to move the shelves to a more suitable spot.

If the wall is hollow. You will not need to spackle it. For to install a toggle you need a hole large enough for the toggle to go through and sometimes the hole needed is a little to large for the item being attached to cover.. This appears as if it could be a factor in the book case you show..

One solution.....

Check for the proper hole size that the toggle will fit through.

If it is smaller and will not show by bookcase frame. Good.

If the hole is larger and would show once the shelf is mounted..

Remove the screw from the toggle.

Place the screw through the shelf frame.

Slide on a Rosette washer. It should be place between the wall and frame.

Install the toggle until two or three threads are shown.

Repeat for the other side of the frame.

Position the shelf to where you can shove the toggles through the holes in the wall. May want a helper for this.

Once both toggles are inside of the wall cavity. Tighten the screws alternating one side then the other until the unit is secured to the wall..

Rosette Washer can also be used if you are on a stud to hide any damage previous screws or drill may have caused with spackling.

Rosette Washers can be gotten at just about any hardware store and they come in many styles and colors.

Are you talking about anchoring a free-standing bookshelf unit (to prevent tipping), or about anchoring the shelf itself to the wall? If the latter, there's no way drywall is going to hold the weight. You need to anchor to a stud. And I would strongly recommend anchoring to a stud even for a free-standing bookshelf.

I agree with DavidR...there is no way I would mount a bookcase on sheetrock unless the screws went directly into studs. You can mount a shelf to sheetrock, but, as once you start loading, it you risk pullout sooner or later.

It's a free-standing bookshelf (https://www.cb2.com/helix-70-acacia-bookcase/s328328)

Basically, two parallel vertical metal "legs" stand 30" apart from each other and 11" from the wall. They have the the shelves screwed to them. Close to the top, the legs bend at 90 degree angles, pointed toward the wall. These are anchored to the wall to prevent the shelf from tipping. The weight of the shelf contents is supported by the vertical "legs"

That should be ok then if you use moly bolts, if there are no studs.

The other solution I see is to add a thin piece of wood stained to match the shelves behind the top anchor bit. Screw the board to a stud and then screw the shelve to the strip. An alternate type of anchor is a much easier solution though.